pub fn new_birthday_probability(n: u32) -> f64 {
    if n < 2 {
        return 0.0;
    }

    let days_in_year = 365;
    let mut prob_no_shared_birthday = 1.0;

    for i in 0..n {
        prob_no_shared_birthday *= (days_in_year - i) as f64 / days_in_year as f64;
    }

    let prob_shared_birthday = 1.0 - prob_no_shared_birthday;
    return (prob_shared_birthday * 10000.0).round() / 10000.0;
}


